In Section  we have proved an existence result of the Cauchy problem for \({\hat{P}}\) , which coincides with the original \(P\)  only in a small conic neighborhood of the reference point. Following [1]}, [2]}, [3]} (also [4]}) we show the micro support of \(u(t,\cdot )\) , obtained by Theorem REF , propagates with a finite speed via estimates of Sobolev norms of \(\Phi u\) , cut off by a suitable \(\Phi \) . This fact enables us to solve the Cauchy problem for the original \(P\)  through that of \({\hat{P}}\) .
